Stochastic homogenization of subdifferential inclusions via scale integration

Marco Veneroni

Abstract


We study the stochastic homogenization of the system

 

   ση ∈ ∂φη η ∈ ∂φη η ∈ ∂φηη ∈ ∂φηdiv ση = (∇uη),

where

 

 

φη is a sequence of convex stationary random fields, with p-growth. We prove that sequences of solutions (ση, uη) converge to the solutions of a deterministic system having the same subdifferential structure. The proof relies on Birkhoff’s ergodic theorem, on the maximal monotonicity of the subdifferential of a convex function, and on a new idea of scale integration, recently introduced by A. Visintin.


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